Existence and asymptotic behaviour of solutions to weakly damped wave equations of Kirchhoff type with nonlinear damping and source terms

DOI10.1016/j.jmaa.2009.07.010zbMath1183.35044OpenAlexW2043814793MaRDI QIDQ1034067

Takeshi Taniguchi

Publication date: 10 November 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2009.07.010

zbMATH Keywords

weak solutionsglobal solutionasymptotic behaviour of solutionslocal weak solutionweakly damped wave equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for higher-order hyperbolic equations (35L35) Integro-partial differential equations (35R09) Higher-order semilinear hyperbolic equations (35L76)

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Cites Work

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• Existence of a solution of the wave equation with nonlinear damping and source terms
• On global solutions and energy decay for the wave equations of Kirchhoff type with nonlinear damping terms
• Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings
• Blowup of solutions of a nonlinear wave equation
• Global existence of solutions to a wave equation with damping and source terms
• Exponential decay of solutions of a nonlinearly damped wave equation
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Blow-up of solutions for the Kirchhoff equation of q-Laplacian type with nonlinear dissipation
• Some remarks on the wave equations with nonlinear damping and source terms
• Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave Equations

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